Abstract
The Van der Pol oscillator is investigated by the parameter control method. This method only needs to control one parameter of the Van der Pol oscillator by a simple periodic function; then, the Van der Pol oscillator can behave chaotically from the stable limit cycle. Based on the new Van der Pol oscillator with variable parameter (VdPVP), some dynamical characteristics are discussed by numerical simulations, such as the Lyapunov exponents and bifurcation diagrams. The numerical results show that there exists a positive Lyapunov exponent in the VdPVP. Therefore, an encryption algorithm is designed by the pseudo-random sequences generated from the VdPVP. This simple algorithm consists of chaos scrambling and chaos XOR (exclusive-or) operation, and the statistical analyses show that it has good security and encryption effectiveness. Finally, the feasibility and validity are verified by simulation experiments of image encryption.
Highlights
Chaos, as one of the three important discoveries of physics in the 20st century, has attracted wide attention
VdPD (Van der Pol-Duffing) Jerk oscillator is proposed based on the Van der Pol–Duffing oscillator and Jerk oscillator, and the dynamic characteristics of the VdPD-Jerk oscillator are investigated by numerical results, such as chaotic attractors and symmetrical bifurcations
This paper aims to study a new chaotic system based on the Van der Pol oscillator by the parameter control method
Summary
As one of the three important discoveries of physics in the 20st century, has attracted wide attention. The modified Van der Pol oscillator and the chaos phenomena of forced oscillation Van der Pol–Duffing equation are investigated by adding an external excitation term [7,8,9,10]. VdPD (Van der Pol-Duffing) Jerk oscillator is proposed based on the Van der Pol–Duffing oscillator and Jerk oscillator, and the dynamic characteristics of the VdPD-Jerk oscillator are investigated by numerical results, such as chaotic attractors and symmetrical bifurcations. The dynamics of symmetric and asymmetric Van der Pol–Duffing oscillators with a periodic force are studied in Reference [12], where the existence of parameter regions are investigated for the periodic, quasiperiodic and chaotic behaviors. An experimental demonstration of a generation of bursting patterns in the Van der Pol oscillator driven by two types of excitation is presented in Reference [14], and the periodic and chaotic bursting oscillations are generated by the slowly sinusoidal voltage source
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